Sequences of regressions and their independences
Artikel i vetenskaplig tidskrift, 2012

Ordered sequences of univariate or multivariate regressions provide statistical models for analysing data from randomized, possibly sequential interventions, from cohort or multi-wave panel studies, but also from cross-sectional or retrospective studies. Conditional independences are captured by what we name regression graphs, provided the generated distribution shares some properties with a joint Gaussian distribution. Regression graphs extend purely directed, acyclic graphs by two types of undirected graph, one type for components of joint responses and the other for components of the context vector variable. We review the special features and the history of regression graphs, prove criteria for Markov equivalence and discuss the notion of a simpler statistical covering model. Knowledge of Markov equivalence provides alternative interpretations of a given sequence of regressions, is essential for machine learning strategies and permits to use the simple graphical criteria of regression graphs on graphs for which the corresponding criteria are in general more complex. Under the known conditions that a Markov equivalent directed acyclic graph exists for any given regression graph, we give a polynomial time algorithm to find one such graph.

equivalence classes

multiplicative models


chain graphs


Concentration graphs

seemingly unrelated regressions



triangular systems

Covariance graphs

Graphical Markov models

Chain graphs


graph markov-models


Nanny Wermuth

Göteborgs universitet

Chalmers, Matematiska vetenskaper, matematisk statistik

K. Sadeghi

University of Oxford


1133-0686 (ISSN)

Vol. 21 215-252


Sannolikhetsteori och statistik